( function () {
/**
 * NURBS utils
 *
 * See NURBSCurve and NURBSSurface.
 **/

/**************************************************************
 *	NURBS Utils
 **************************************************************/

class NURBSUtils {
  /*
  Finds knot vector span.
  	p : degree
  u : parametric value
  U : knot vector
  	returns the span
  */
  static findSpan(p, u, U) {
    const n = U.length - p - 1;

    if (u >= U[n]) {
      return n - 1;
    }

    if (u <= U[p]) {
      return p;
    }

    let low = p;
    let high = n;
    let mid = Math.floor((low + high) / 2);

    while (u < U[mid] || u >= U[mid + 1]) {
      if (u < U[mid]) {
        high = mid;
      } else {
        low = mid;
      }

      mid = Math.floor((low + high) / 2);
    }

    return mid;
  }
  /*
  Calculate basis functions. See The NURBS Book, page 70, algorithm A2.2
  	span : span in which u lies
  u    : parametric point
  p    : degree
  U    : knot vector
  	returns array[p+1] with basis functions values.
  */


  static calcBasisFunctions(span, u, p, U) {
    const N = [];
    const left = [];
    const right = [];
    N[0] = 1.0;

    for (let j = 1; j <= p; ++j) {
      left[j] = u - U[span + 1 - j];
      right[j] = U[span + j] - u;
      let saved = 0.0;

      for (let r = 0; r < j; ++r) {
        const rv = right[r + 1];
        const lv = left[j - r];
        const temp = N[r] / (rv + lv);
        N[r] = saved + rv * temp;
        saved = lv * temp;
      }

      N[j] = saved;
    }

    return N;
  }
  /*
  Calculate B-Spline curve points. See The NURBS Book, page 82, algorithm A3.1.
  	p : degree of B-Spline
  U : knot vector
  P : control points (x, y, z, w)
  u : parametric point
  	returns point for given u
  */


  static calcBSplinePoint(p, U, P, u) {
    const span = this.findSpan(p, u, U);
    const N = this.calcBasisFunctions(span, u, p, U);
    const C = new THREE.Vector4(0, 0, 0, 0);

    for (let j = 0; j <= p; ++j) {
      const point = P[span - p + j];
      const Nj = N[j];
      const wNj = point.w * Nj;
      C.x += point.x * wNj;
      C.y += point.y * wNj;
      C.z += point.z * wNj;
      C.w += point.w * Nj;
    }

    return C;
  }
  /*
  Calculate basis functions derivatives. See The NURBS Book, page 72, algorithm A2.3.
  	span : span in which u lies
  u    : parametric point
  p    : degree
  n    : number of derivatives to calculate
  U    : knot vector
  	returns array[n+1][p+1] with basis functions derivatives
  */


  static calcBasisFunctionDerivatives(span, u, p, n, U) {
    const zeroArr = [];

    for (let i = 0; i <= p; ++i) zeroArr[i] = 0.0;

    const ders = [];

    for (let i = 0; i <= n; ++i) ders[i] = zeroArr.slice(0);

    const ndu = [];

    for (let i = 0; i <= p; ++i) ndu[i] = zeroArr.slice(0);

    ndu[0][0] = 1.0;
    const left = zeroArr.slice(0);
    const right = zeroArr.slice(0);

    for (let j = 1; j <= p; ++j) {
      left[j] = u - U[span + 1 - j];
      right[j] = U[span + j] - u;
      let saved = 0.0;

      for (let r = 0; r < j; ++r) {
        const rv = right[r + 1];
        const lv = left[j - r];
        ndu[j][r] = rv + lv;
        const temp = ndu[r][j - 1] / ndu[j][r];
        ndu[r][j] = saved + rv * temp;
        saved = lv * temp;
      }

      ndu[j][j] = saved;
    }

    for (let j = 0; j <= p; ++j) {
      ders[0][j] = ndu[j][p];
    }

    for (let r = 0; r <= p; ++r) {
      let s1 = 0;
      let s2 = 1;
      const a = [];

      for (let i = 0; i <= p; ++i) {
        a[i] = zeroArr.slice(0);
      }

      a[0][0] = 1.0;

      for (let k = 1; k <= n; ++k) {
        let d = 0.0;
        const rk = r - k;
        const pk = p - k;

        if (r >= k) {
          a[s2][0] = a[s1][0] / ndu[pk + 1][rk];
          d = a[s2][0] * ndu[rk][pk];
        }

        const j1 = rk >= -1 ? 1 : -rk;
        const j2 = r - 1 <= pk ? k - 1 : p - r;

        for (let j = j1; j <= j2; ++j) {
          a[s2][j] = (a[s1][j] - a[s1][j - 1]) / ndu[pk + 1][rk + j];
          d += a[s2][j] * ndu[rk + j][pk];
        }

        if (r <= pk) {
          a[s2][k] = -a[s1][k - 1] / ndu[pk + 1][r];
          d += a[s2][k] * ndu[r][pk];
        }

        ders[k][r] = d;
        const j = s1;
        s1 = s2;
        s2 = j;
      }
    }

    let r = p;

    for (let k = 1; k <= n; ++k) {
      for (let j = 0; j <= p; ++j) {
        ders[k][j] *= r;
      }

      r *= p - k;
    }

    return ders;
  }
  /*
  	Calculate derivatives of a B-Spline. See The NURBS Book, page 93, algorithm A3.2.
  		p  : degree
  	U  : knot vector
  	P  : control points
  	u  : Parametric points
  	nd : number of derivatives
  		returns array[d+1] with derivatives
  	*/


  static calcBSplineDerivatives(p, U, P, u, nd) {
    const du = nd < p ? nd : p;
    const CK = [];
    const span = this.findSpan(p, u, U);
    const nders = this.calcBasisFunctionDerivatives(span, u, p, du, U);
    const Pw = [];

    for (let i = 0; i < P.length; ++i) {
      const point = P[i].clone();
      const w = point.w;
      point.x *= w;
      point.y *= w;
      point.z *= w;
      Pw[i] = point;
    }

    for (let k = 0; k <= du; ++k) {
      const point = Pw[span - p].clone().multiplyScalar(nders[k][0]);

      for (let j = 1; j <= p; ++j) {
        point.add(Pw[span - p + j].clone().multiplyScalar(nders[k][j]));
      }

      CK[k] = point;
    }

    for (let k = du + 1; k <= nd + 1; ++k) {
      CK[k] = new THREE.Vector4(0, 0, 0);
    }

    return CK;
  }
  /*
  Calculate "K over I"
  	returns k!/(i!(k-i)!)
  */


  static calcKoverI(k, i) {
    let nom = 1;

    for (let j = 2; j <= k; ++j) {
      nom *= j;
    }

    let denom = 1;

    for (let j = 2; j <= i; ++j) {
      denom *= j;
    }

    for (let j = 2; j <= k - i; ++j) {
      denom *= j;
    }

    return nom / denom;
  }
  /*
  Calculate derivatives (0-nd) of rational curve. See The NURBS Book, page 127, algorithm A4.2.
  	Pders : result of function calcBSplineDerivatives
  	returns array with derivatives for rational curve.
  */


  static calcRationalCurveDerivatives(Pders) {
    const nd = Pders.length;
    const Aders = [];
    const wders = [];

    for (let i = 0; i < nd; ++i) {
      const point = Pders[i];
      Aders[i] = new THREE.Vector3(point.x, point.y, point.z);
      wders[i] = point.w;
    }

    const CK = [];

    for (let k = 0; k < nd; ++k) {
      const v = Aders[k].clone();

      for (let i = 1; i <= k; ++i) {
        v.sub(CK[k - i].clone().multiplyScalar(this.calcKoverI(k, i) * wders[i]));
      }

      CK[k] = v.divideScalar(wders[0]);
    }

    return CK;
  }
  /*
  Calculate NURBS curve derivatives. See The NURBS Book, page 127, algorithm A4.2.
  	p  : degree
  U  : knot vector
  P  : control points in homogeneous space
  u  : parametric points
  nd : number of derivatives
  	returns array with derivatives.
  */


  static calcNURBSDerivatives(p, U, P, u, nd) {
    const Pders = this.calcBSplineDerivatives(p, U, P, u, nd);
    return this.calcRationalCurveDerivatives(Pders);
  }
  /*
  Calculate rational B-Spline surface point. See The NURBS Book, page 134, algorithm A4.3.
  	p1, p2 : degrees of B-Spline surface
  U1, U2 : knot vectors
  P      : control points (x, y, z, w)
  u, v   : parametric values
  	returns point for given (u, v)
  */


  static calcSurfacePoint(p, q, U, V, P, u, v, target) {
    const uspan = this.findSpan(p, u, U);
    const vspan = this.findSpan(q, v, V);
    const Nu = this.calcBasisFunctions(uspan, u, p, U);
    const Nv = this.calcBasisFunctions(vspan, v, q, V);
    const temp = [];

    for (let l = 0; l <= q; ++l) {
      temp[l] = new THREE.Vector4(0, 0, 0, 0);

      for (let k = 0; k <= p; ++k) {
        const point = P[uspan - p + k][vspan - q + l].clone();
        const w = point.w;
        point.x *= w;
        point.y *= w;
        point.z *= w;
        temp[l].add(point.multiplyScalar(Nu[k]));
      }
    }

    const Sw = new THREE.Vector4(0, 0, 0, 0);

    for (let l = 0; l <= q; ++l) {
      Sw.add(temp[l].multiplyScalar(Nv[l]));
    }

    Sw.divideScalar(Sw.w);
    target.set(Sw.x, Sw.y, Sw.z);
  }

}

THREE.NURBSUtils = NURBSUtils;
} )();
